Method for determining thermo-physical properties of specimens

ABSTRACT

The square root of the product of thermophysical properties Rho , c and k, where Rho is density, c is specific heat and k is thermal conductivity, is determined directly on a test specimen such as a wind tunnel model. The test specimen and a reference specimen of known specific heat are positioned a given distance from a heat source. The specimens are provided with a coating, such as a phase change coating, to visually indicate that a given temperature has been reached as well as to ensure that both specimens have the same absorbtivity and thus receive the same heat rate. A shutter interposed between the heat source and the specimens is opened and a motion picture camera is actuated to provide a time record of the heating step. The temperature of the reference specimen is recorded as a function of time. The heat rate to which both the test and reference specimens have been subjected is determined from the temperature time response of the reference specimen by the conventional thin-skin calorimeter equation. This heat rate is then used to determine square root Rho ck of the test specimen from the transient one dimensional heat conduction equation for a semi-infinite solid subjected to a step heat input at a constant heat rate. A model, such as a wind tunnel model, can be tested directly thus eliminating the costly and inaccurate method of making test models solely for the purpose of determining square root Rho ck.

United States Patent [191 Jones [4 1 Feb. 5, 1974 METHOD FOR DETERMINING THERMO-PHYSICAL PROPERTIES OF SPECIMENS [75] Inventor: Robert A. Jones, Newport News,

[73] Assignee: The United States of America as represented by the Administrator of the National Aeronautics and Space Administration, Washington, DC.

[22] Filed: Aug. 18, 1972 [21] Appl. No.: 281,875

[52] US. Cl 73/15 R [51] Int. Cl. GOln 25/18 [58] Field of Search 73/15, 190

[56] References Cited UNITED STATES PATENTS 3,570,302 3/1971 Saver 73/15 3,165,915 l/l965 Parker 73/15 3,279,239 10/1966 Arends et a1. 73/15 3,566,669 3/1971 Lawrence et a1. 73/15 3,433,052 3/1969 Maley 73/15 3,114,836 12/1963 Fergason et al. 73/356 Primary Examiner-Herbert Goldstein Attorney, Agent, or Firm-Howard J. Osborn; Wallace J. Nelson; John R. Manning HEAT SOURCE CAMERA 57] ABSTRACT The square root of the product of thermophysical properties p, c and k, where p is density, 0 is specific heat and k is thermal conductivity, is determined directly on a test specimen such as a wind tunnel model. The test specimen and a reference specimen of known specific heat are positioned a given distance from a heat source. The specimens are provided with a coating, such as a phase change coating, to visually indicate that a given temperature has been reached as well as to ensure that both specimens have the same ab sorbtivity and thus receive the same heat rate. A shutter interposed between the heat source and the specimens is opened and a motion picture camera is actuated to provide a time record of the heating step. The temperature of the reference specimen is recorded as a function of time. The heat rate to which both the test and reference specimens have been subjected is determined from the temperature time response of the reference specimen by the conventional thin-skin calorimeter equation. This heat rate is then used to determine V p ck of the test specimen from the transient one dimensional heat conduction equation for a semiinfinite solid subjected to a step heat input at a constant heat rate. A model, such as a wind tunnel model, can be tested directly thus eliminating the costly and inaccurate method of making test models solely for the purpose of determining V p 01?.

' 9 l aimgl Drawing Figure IONSAMPLE REFERENCE 2 PATENTED FEB 74 CAMERA shiwsw REFERENCE l2 RECORDER METHOD FOR DETERMINING THERMO-PIIYSICAL PROPERTIES OF SPECIMENS BACKGROUND OF THE INVENTION This invention relates to a method and apparatus for determining .V p ck, the square root of the product of thermophysical properties, p,c, and k, for a specimen.

Experimental aerodynamicists are presently relying extensively on the phase-change coating technique for measuring aerodynamic heat transfer to small complex wind tunnel models. This simple and useful technique employs a model made from a low-conductivity material usually plastic. The accuracy of the data obtained with this technique depends directly upon the accuracy with which the parameter V p ck, is known; p being the density, c being the specific heat, and k being the thermal conductivity. The value of V p ck varies from model to model as well as with temperature and even depth (in non-homogeneous materials) into the model material. Thus, it has been necessary in the past to make samples for each model cast and to measure p, c, and k over a range of temperatures to obtain even acceptable accuracy with the phase-change technique. At the present time such measurements are being made using standard techniques for measurement. There are several major disadvantages of this known method.

. Thestandard techniques (see for example the paper Thermophysical Properties Measurements Performed for NASA? by H.L. Traiger and R.L. Wentworth Dynateck Corp. Aug. 27, 1964) require elaborate equipment, specially trained technicians, and samples instrumented with thermocouples. The fabrication of samples and instrumenting them with thermocouples costs about as much as building a complex wind tunnel model.

Considerable time is required to instrument the thermal conductivity sample with thermocouples and the measurements are usually made in laboratories specializing in this type of work which requires sending the samples elsewhere for analysis. It often happens that wind tunnel tests are completed and the data reduced before the thermophysical properties are available.

There are several factors which make the conventional techniques less accurate than desired. These are:

a. the standard techniques now employed measure p, c, and k independently so that the accuracy in the product Vp ck is the product of the inaccuracies of the individual measurements;

b. the measurements are made on samples of the model material, not the model itself and there may very well be differences between the properties of the model and that of the samples;

c. the standard techniques measure an average value BRIEF SUMMARY The foregoing and other objects which will be apparent to those of ordinary skill in the art are achieved according to the present invention by providing a method for determining the value of the square root of the product of thermophysical properties vm of a material including the steps of providing a test specimen of a material to be tested, providing a reference specimen of a material having a known specific heat, subjecting a surface of the test and reference specimens simultaneously to a heat source located a given dis- .tance from the test and reference specimens said surfaces having the same absorptivity such that the test and reference specimens are subjected to the same heat rate, determining the time required to heat the reference specimen to a given temperature, determining the time required to heat the test specimen to the given temperature, measuring the temperature of the reference specimen as a function of time to determine the rate of change of temperature thereof with time, determining the heat rate to which the test and reference specimens were subjected, and determining from the heat rate the value of the square root of the product of thermophysical properties Vp ck for the specimen. Apparatus for carrying out the method includes a heat source, means for locating a test specimen of a material to be tested a given distance from the heat source, means for locating a reference specimen of a material having a known specific heat the given distance from the heat source, means for exposing the test and reference specimens to the heat source, means for determining the time required to heat the test specimen to a given temperature, means for determining the time required to heat the reference specimen to the given temperature, and means for measuring the temperature of the reference specimen as a function of time.

DETAILED DESCRIPTION There follows a detailed description of a preferred embodiment of the invention, together with an accompanying drawing. However, it is to be understood that the detailed description and accompanying drawing are provided solely for the purpose of illustrating a preferred embodiment and that the invention is capable of numerous modifications and variations apparent to those skilled in the art without departing from the spirit and scope of the invention.

The drawing is a diagrammatic plan view of apparatus according to the invention.

A model 10, or a specimen of the model material, is provided with a coating 11 of Tempilaq phasechange temperature indicator having a melt temperature of the desired temperature of calibration. In this case the coatings may have a melt temperature in the range from F to 500 F. A reference specimen 12 is made by coating a layer 13 of the same phase-change temperature indicator material on a thin sheet of stainless steel 14. Reference specimen 12, of course, is not the same material as that of model 10. A thermocouple 15 is welded to the rear side of sheet 14. By utilizing the same temperature indicator coating material on both specimens, the emissivity is the same thus insuring that both are subjected to the same heating rate. The test .and reference specimens are located a given distance from radiant heat source 16, in this case a plurality of quartz heating lamps, only one of which is shown. The

specimens may be located in this position by suitable indicia provided on a table top, by holding clamps, or the like.

A shutter 17, which can simply be in the form of two moveable plates 18, 19, is interposed between heat source 16 and the specimens and 12.

A motion picture camera 20 having a known frame speed is positioned to photograph the front surfaces (that is the surfaces facing heat source of the specimens on which surfaces the temperature indicating coatings are provided. Thermocouple leads 21, 22 are attached to a conventional recorder 23 which receives the electrical signal generated by thermocouple 14 and records temperature (or an electrical signal proportional thereto) as a function of time.

To calculate the value Vp ck, quartz lamp 16 is turned on and, in this particular case, has a temperature in the range from 1,500 F to 5,000 F. It is desirable to keep the temperature of the heat source substantially higher than the highest temperature for which V p ck is to be determined so that the change in temperature of the heated specimens-will have a negligible effect on the imposed heat rate. A difference in temperature of at least l,000 F is preferred. lnitial temperature may be obtained by use of a conventional surface contact thermometer (not shown) or by any other conventional technique.

Motion picture camera is started and shutter 17 is then rapidly opened to subject both specimens to a step input in radiative heat. The time required for the surface of the specimens to reach the phase change temperature, in this case a temperature in the range of 125 F to 500 F, is determined from the motion picture film record which is taken at a known frame rate.

The heat rate to which both specimens was subjected is then determined from the temperature-time response of thermocouple 15 on the back side of the reference specimen by the thin skin calorimeter equation:

where Q heat rate,

p density of stainless steel sheet 12,

specific heat of stainless steel sheet 12,

l= thickness of stainless steel sheet 12, and

dT/dt rate of change of temperature of stainless steel sheet 12 with time.

With this known heat rate, the value of V p ck is determined from the transient one dimensional heat conduction equation for a semi-infinite solid subjected to a step input at a constant heat rate:

where T phase-change temperature Ti initial specimen temperature, and

I, time required for phase change to occur in coating 11 on test specimen 10.

In a specific example of the invention, the properties of reference heat gauge are as follows:

p 494.2 lbs/ft C 0.1383, Btu/(117 F) The temperature-time history of reference heat gauge is as follows:

I, secs. T "F 19016 75.7 191.01 75.7 192.01 77.2 193.09 78.5 193.91 79.4 194.50 80.2 195.19 81.] 195.96 82.0 197.135 83.5 198.01 84.5 198.885 85.5 199.76 86.2 200.635 87.0

The rate of change of temperature with respect to time of the reference heat guage, dT /dt, is found by fitting a curve to the above data and taking the derivative:

dT /dt 1.127" F/sec.

The reference heating rate is then found by equation 1:

Q 494.2 lbs/ft 0.1383 Btu/(1b F) X 0.000395 ft X 1.127 F/sec Q 0.3042 Btu/(ft sec.)

The test conditions for the model specimen are:

t,,,=4.8 secs.

The square root of the thermophysical properties,

Vp ck, is then found by equation (2):

Vp ck 0.3042 Btu/(ft sec)/l03 F 75.7 F (2/ V?) V4.8 secs.

Vp ck 0.0275 Btu/(ft F sec H2) The value of V pck can be determined according to the invention for various melt times by either using different phase-change coatings or by changing the imposed heat rate, or both. The heat rate is conveniently changed by changing the number of heat lamps used or the lamp temperature or both. In this manner, the value of V pck can be determined for various depths of heat penetration into the model surface.

It will be seen from the foregoing that the disadvantages associated with previously known methods have been overcome by the present invention. The actual test model can be used to determine Vpck directly without determining the individual values of p, c, and k.

What is claimed is:

l. A method of determining the value of the square r q9 t of the product of thermophysical properties v m of a material comprising the steps of: I

providing a test specimen of a material to be tested;

providing a reference specimen of a material having a known specific heat, thickness and density;

subjecting a surface of the test and reference specimens of known initial temperature simultaneously to a heat source located a given distance from the test and reference specimens, said surfaces having the same absorptivity such that the test'and reference specimens are subjected to the same heat rate;

determining the time required to heat the reference specimen to a given temperature;

determining the time required to heat the test specimen to said given temperature; measuring the temperature of said reference specimen as a function of time to determine the rate of change of temperature thereof with time;

determining the heat rate to which the test and reference specimens were subjected; and

determining from said heat rate the value of the product of thermophysical properties V pck for said specimen.

2. A method according to claim 1 wherein the test and reference specimens are each provided with means for visually indicating that said given temperature has been reached.

3. A method according to claim 2 wherein the time required to heat the reference and test specimens to said given temperature is determined by visual observation.

4. A method according to claim 2 wherein the time required to heat the reference and test specimens to said given temperature is determined by providing a motion picture record of the heating step and by analysis of the developed photographic record.

5. A method according to claim 2 wherein said visual where Q the heat rate Tg the given temperature Ti the initial temperature of the specimens,

t= time required for test specimen to reach the given temperature.

8. A method according to claim l wherein said heat source comprises a radient heat source.

9. A method according to claim 1 wherein the temperature of said heat source is sufficiently higher than said given temperature that the change in temperature of the specimens has a negligible effect on the imposed heat rate. 

1. A method of determining the value of the square root of the product of thermophysical properties square root Rho ck of a material comprising the steps of: providing a test specimen of a material to be tested; providing a reference specimen of a material having a known specific heat, thickness and density; subjecting a surface of the test and reference specimens of known initial temperature simultaneously to a heat source located a given distance from the test and reference specimens, said surfaces having the same absorptivity such that the test and reference specimens are subjected to the same heat rate; determining the time required to heat the reference specimen to a given temperature; determining the time required to heat the test specimen to said given temperature; measuring the temperature of said reference specimen as a function of time to determine the rate of change of temperature thereof with time; determining the heat rate to which the test and reference specimens were subjected; and determining from said heat rate the value of the product of thermophysical properties square root Rho ck for said specimen.
 2. A method according to claim 1 wherein the test and reference specimens are each provided with means for visually indicating that said given temperature has been reached.
 3. A method according to claim 2 wherein the time required to heat the reference and test specimens to said given temperature is determined by visual observation.
 4. A method according to claim 2 wherein the time required to heat the reference and test specimens to said given temperature is determined by providing a motion picture record of the heating step and by analysis of the developed photographic record.
 5. A method according to claim 2 wherein said visual indicating means comprises a phase change coating.
 6. A method according to claim 1 wherein said heat rate is determined from the equation: Q Rho c l dT/dt wherein Q heat rate, Rho density of the reference specimen, c specific heat of the reference specimen, l thickness of the reference specimen; and dT/dt rate of change of temperature of the reference specimen with time.
 7. A method according to claim 1 wherein the value of Square Root Rho ck is determined from the following equation: Square Root Rho ck Q/Tg - Ti . (2/ Square Root pi ) . Square Root t where Q the heat rate Tg the given temperature Ti the initial temperature of the specimens, t time required for test specimen to reach the given temperature.
 8. A method according to claim 1 wherein said heat source comprises a radient heat source.
 9. A method according to claim 1 wherein the temperature of said heat source is sufficiently higher than said given temperature that the change in temperature of the specimens has a negligible effect on the imposed heat rate. 